数学物理

We define $2n$-multiwebs on planar graphs and discuss their relation with $\mathrm{Sp}(2n)$-webs. On a planar graph with a symplectic local system we define a matrix whose Pfaffian is the sum of traces of $2n$-multiwebs. As application we…

For the KdV equation with well-type initial value, the interaction between the trial soliton and the mean field is studied. The well initial value will lead to the appearance of rarefaction wave and dispersion shock wave, and there will be…

The $\lambda$-differential operators and modified $\lambda$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $\lambda$-differential Poisson ($\lambda$-DP for short)…

In a series of recent scientific contributions the role of bosonic and fermionic ladder operators in a macroscopic realm has been investigated. Creation, annihilation and number operators have been used in very different contexts, all…

The Cauchy problem for semi-linear Klein-Gordon equations is considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. The local and global well-posedness of the Cauchy problem is considered in Sobolev spaces. The non-existence of…

We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting factor"). If the twisting factor is fundamental…

We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain in terms of Sobolev spaces and their duals. Any one-particle density that is square-integrable, has a…

We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses…

We provide an overview of basic concepts, tools, and results of quantum field theoretical scattering theory. This article is prepared for the second edition of the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo,…

We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…

We consider the anyonic spin systems with a global symmetry, the so-called symmetry enriched topological (SET) phases. We introduce the phase characterizing the symmetry fractionalization of the anyons. Our assumptions on how the global…

An algorithm is provided to tile the plane with the aperiodic monotile Tile(1,1) recently discovered by Smith et al. (2023). Their geometric construction guidelines are expanded into a numerical MATLAB algorithm. The intention is to remove…

In the literature, abelian higher gauge symmetry models are shown to be valid in all finite dimensions and exhibit the characteristic behavior of SPT phases models. While the ground state degeneracy and the entanglement entropy were…

We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-Powell, Liu, and Shamis-Sodin for long-range operators with…

In this paper we construct a family of topological conformal field theories (TCFTs) associated to a Calabi-Yau space by modifying the heat kernel and sections of the Calabi-Yau space. This is done by restricting to certain eigenspaces of…

We study the Hankel determinant generated by the moments of the deformed Laguerre weight function $x^{\alpha}{\rm{e}}^{-x}\prod\limits_{k=1}^{N}(x+t_k)^{\lambda_k}$, where $x\in \left[0,+\infty \right)$, $\alpha,t_k >0,…

We consider a neutral bosonic molecule in the Born-Oppenheimer approximation without spin and assume the physically obvious assertion that a neutral molecule prefers to break into smaller neutral clusters. We prove the existence of a global…

In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie…

In this article we generalize the discrete Lagrangian and Hamiltonian mechanics on Lie groups to non-associative objects generalizing Lie groups (smooth loops). This shows that the associativity assumption is not crucial for mechanics and…

This work is devoted to the causal perturbative Quantum Field Theory (QFT) due to Bogoliubov, including QED and other realistic QFT. It is given the white noise formulation of this theory. The white noise analysis and the Hida operators as…